Rabbits are not suitable for children because their hind legs are too strong for their backs. They are prey animals, so are not happy being picked up as they fear they'll be eaten. If they're not held strongly enough, and they kick out trying to flee they can break their spines. Also, if they're dropped, the same thing can happen.
They can be temperamental. The one I had as a teenager would bite, once going through my mother's thumbnail. I still have scars on my hand from her, 20 years later.
They are destructive. The garden is full of warrens: it has taken a lot of money to build a run they can't escape from. In the house they chew wires, carpet, books, basically anything they can find. I have had two indoors recuperating for the last few months and I dread finding out how much damage they've caused when I finally get them outside.
On the plus side, they can be litter-trained (within reason), and are wonderful animals. Whoever coined the phrase "curiosity killed the cat" had obviously never met a rabbit. They like to stick their noses in everything! I wouldn't be without the wee beggers, but I fully accept the downsides.
Guinea pigs are also adorable, but are less likely to be housetrained. They are less hardy than rabbits, so my lot spend much of the year in the house, in a cage. They are highly vocal, and impossible to forget to feed! They're more handable than rabbits, but I still wouldn't let a young child pick them up (last one who attempted it go a major telling off from me). They're more expensive to feed, though, as they need a range of fresh fruit and veg every day, due to their inability to synthesise vitamin C.